Air Conditioner Blows Hot When Stopped?

My car's air conditioner works great and blows cold when my foot is on the gas pedal. Once I step on the brakes, the air conditioner sounds like it's shutting off (makes a hissing noise) and then starts blowing hot/humid air. I can hear a groaning noise coming from somewhere below the car, but I'm not sure where it's coming from- just that I only hear it once the air blows hot when I'm on the brakes. Occasionally I can feel the brake pedal twitch under my foot, no matter how hard I hold it down, and it causes the car to jerk forward an inch or two. If I'm constantly on the brakes (stop-and-go traffic), the temperature gauge will rise pretty quickly and then eventually the red check gauge light comes on once the temperature gauge is almost maxed out. Once you step on the gas, the temperature drops back down, the check gauge light goes off, and the air starts blowing cold again like nothing ever happened.